Prove that a tree in which every vertex has degree at most 2 is a simple path. More precisely:
Let $G = (V,E)$ be an undirected tree, with $|V| = n \geq 1$ and assume that every vertex has degree at most $2$. Then $V$ can be ordered into a simple path $\langle v_1 ..... , v_n\rangle$ and it uses all edges in $E$.
I'm not sure how to even start with this problem here. So a tree is a graph such that it has no cycles and this particular tree has vertex's with degree AT MOST 2. That means that the first and last vertex will have 1 edge and every vertex in between will have 2. That should be a simple path. I don't know how to prove this formally. Any help? should I be using an adjacency matrix anywhere?